Topological polynomial and indices based on the distance between vertices of a connected graph are widely used in chemistry to establish relation structure properties molecules. In similar way, chromatic versions certain topological related have also been discussed recent literature. this paper, we present Schultz Gutman polynomials expanded form Hosoya polynomials, then derive these for specia...

Please cite this article as: P.K. Douglas, Boris Gutman, Ariana Anderson, C. Larios, Katherine E. Lawrence, Katherine Narr, Biswa Sengupta, Gerald Cooray, David B. Douglas, Paul M. Thompson, James J. McGough, Susan Y. Bookheimer , Hemispheric brain asymmetry differences in youths with attention-deficit/hyperactivity disorder. The address for the corresponding author was captured as affiliation ...

Karl H. Schuleri, Luciano C. Amado, Andrew J. Boyle, Marco Centola, Anastasios P. Saliaris, Matthew R. Gutman, Konstantinos E. Hatzistergos, Behzad N. Oskouei, Jeffrey M. Zimmet, Randell G. Young, Alan W. Heldman, Albert C. Lardo, and Joshua M. Hare Division of Cardiology, Department of Medicine and Institute for Cell Engineering, Johns Hopkins University School of Medicine and Osiris Therapeut...

Recently, based on elementary geometry, Gutman proposed several geometry-based invariants (i.e., $SO$, $SO_{1}$, $SO_{2}$, $SO_{3}$, $SO_{4}$, $SO_{5}$, $SO_{6}$). The Sombor index was defined as $SO(G)=\sum\limits_{uv\in E(G)}\sqrt{d_{u}^{2}+d_{v}^{2}}$, the first $SO_{1}(G)= \frac{1}{2}\sum\limits_{uv\in E(G)}|d_{u}^{2}-d_{v}^{2}|$, where $d_{u}$ denotes degree of vertex $u$. In this paper, w...

We present estimates on the small singular values of a class of matrices with independent Gaussian entries and inhomogeneous variance profile, satisfying a broad-connectedness condition. Using these estimates and concentration of measure for the spectrum of Gaussian matrices with independent entries, we prove that for a large class of graphs satisfying an appropriate expansion property, the Bar...

Patentee(s): Yissum Research Development Company of The Hebrew University of Jerusalem of Hi Tech Park Edmond Safra Campus Givat-Ram PO Box 39135 Jerusalem 91390 Israel Inventor(s): Rav-Acha, Alexander Pritch, Yael Peleg, Shmuel Gutman, Avital Title: Method and system for video indexing and video synopsis Term: Twenty years from 9 December 2007 Date Accepted: 21 October 2011 Date Sealed: 23 Feb...

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene polycyclic aromatic compounds. Recently, A family Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these may be successfully applied on modeling thermodynamic properties In this paper, we study expected values random hexagonal chains, consider some graphs such as g...

For a graph G we denote by dG(u, v) the distance between vertices u and v in G, by dG(u) the degree of vertex u. The Hosoya polynomial of G is H(G) = ∑ {u,v}⊆V (G) x dG (u,v). For any positive numbers m and n, the partial Hosoya polynomials of G are Hm(G) = ∑ {u, v} ⊆ V (G) dG (u) = dG (v) = m xdG (u,v), Hmn(G) = ∑ {u, v} ⊆ V (G) dG (u) = m, dG (v) = n xdG (u,v). It has been shown that H(G1) − ...

Let [Formula: see text] be a simple graph with vertices, edges having Laplacian eigenvalues text]. The energy LE[Formula: is defined as text], where the average degree of Radenković and Gutman conjectured that among all trees order path has smallest energy. family diameter In this paper, we show any tree greater than thereby proving conjecture for We also truth number non-pendent vertices at mo...